Today, we will consider the Hidden Markov Model (HMM). For this, we will first introduce the fully observed (toric) HMM and show how to establish corresponding maximum likelihood estimates.
Second, we will introduce the HMM. By decomposing the marginal probabilities in a sum of products, we obtain by tropicalization the Viterbi algorithm, which provides to each output sequence a state sequence that most likely produced the output sequence.
As an example, we will consider the computation of CpG islands in genomic sequences.
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